In this final section, we construct a non-trivial zero for the functional \({F}\)  defined by (). It is obtained by a Nash-Moser iteration procedure. At each step, we can find an approximate right inverse of the linearized operator following the construction explained in the previous subsection. The proof is technical and already detailed in the previous works [1]}, [2]}, [3]}. Here, we may use the version exposed in [3]}.
